Tensile Test Calculator: Yield Strength, UTS, Elongation and Reduction of Area

Strength, ductility and true stress from the results of a tensile test.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the original diameter and gauge length of the test piece, the load at yield (or at the 0.2 % offset), the maximum load, the load at fracture, and the length and neck diameter after fracture. The calculator gives the yield strength, the ultimate tensile strength (UTS), the yield to tensile ratio, the percentage elongation and the reduction of area.

It also gives the true fracture stress and strain (which use the area at the neck), the elastic strain at yield, the 0.2 % offset strain, and the modulus of resilience, and sketches the stress-strain curve through your points. Strength tells you how much load the material takes; elongation and reduction of area tell you how ductile it is.

Use it for test reports and for checking material certificates. Quote the gauge length with the elongation, as it depends on it.

Formulas used

  • \sigma = \frac{F}{A_0}
  • \text{elongation} = \frac{L_f - L_0}{L_0}
  • \text{reduction of area} = \frac{A_0 - A_f}{A_0}

Worked example

With the default numbers in the calculator above:

  1. Original cross-section area: 122.72 mm²
  2. Yield strength (engineering stress at yield): 244.46 MPa
  3. Ultimate tensile strength (UTS): 366.69 MPa
  4. Yield to tensile ratio: 0.6667
  5. Engineering stress at fracture: 293.35 MPa
  6. Percentage elongation after fracture: 26.00 %
  7. Percentage reduction of area: 53.76 %
  8. True fracture stress (load over the final area): 634.42 MPa
  9. True strain at fracture: 0.7713
  10. Elastic strain at yield, and the 0.2 % offset strain: 0.1222 % elastic, 0.3222 % at the offset
  11. Modulus of resilience (elastic energy per unit volume): 0.1494 MJ/m³
  12. True stress at the maximum load (uniform elongation applied): 425.36 MPa

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What is the 0.2 % offset yield?

Where there is no clear yield point, it is the stress at which a line parallel to the elastic slope, shifted by 0.2 % strain, cuts the curve.

Why is the true stress higher?

True stress uses the actual area, which has necked down, so the same load gives a higher stress than the engineering value based on the original area.

What is a good elongation?

Over 15 % is ductile. Structural steels usually need 18 to 20 %.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 1391 (metallic materials, tensile testing at ambient temperature); Callister, Materials Science and Engineering (mechanical properties of metals).

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